A transient nuclear Overhauser effect (NOE) makes measurements of the 1 3 C spin-lattice relaxation times in organic solids complicated. Extended Solomon equations are applied in order to describe 1 3 C spin-lattice relaxation with 1 H r.f. field irradiation. Spin-lattice relaxation under r.f. irradiation is shown to be generally a triple-exponential process, but it can be reduced to be single-exponential under stronger r.f. field irradiation as well as in the absence of 1 H initial magnetizations. Based on numerical calculations, the difference between spin-lattice relaxation curves obeying T C 1 <T H 1 and those obeyingT C 1 > T H 1 is clearly indicated. The methyl group resonances in solid-statel -valine are examined, and the experimental results agree well with the theoretical results.